Question

find the remainder when x^100-1 is divided by x-1.​

Answer 1

Answer:

Originally Answered: What is the reminder when, x^100 is divided by (x+1)? Let us assume our dividend function to be f(x) and divisor function as g(x). x+1=0 => x=-1 is a root. Thus the the remainder is 1.

Answer 2

The remainder when x¹⁰⁰-1 is divided by x-1 = 0

Given:

Equation x¹⁰⁰-1 is divided by (x-1)

To find:

The remainder when x¹⁰⁰-1 is divided by x-1

Solution:

Note:

According to Remainder Theorem of Euclidean division of polynomials

If a polynomial P(x) is divided by (x-a) then the reminder will be equals to p(a)

Given x¹⁰⁰-1 is divided by x-1

Take  x - 1 = 0

⇒ x = 1

Now substitute x = 1 in given equation  

⇒  x¹⁰⁰-1 =  (1)¹⁰⁰-1 = 1 - 1 = 0

The remainder when x¹⁰⁰-1 is divided by x-1 = 0

#SPJ2